Mathematical Analysis 1
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This is a grouped course. It consists of several seperate subjects that share learning materials, assignments, tests etc. Below you can see information about the individual subjects that make up this subject.
Mathematical Analysis 1 (Main course) B0B01MA1
Credits | 7 |
Semesters | Both |
Completion | Assessment + Examination |
Language of teaching | Czech |
Extent of teaching | 4P+2S |
Annotation
The aim of the course is to introduce students to basics of differential and integral calculus of functions of one variable.
Study targets
The aim of the course is to introduce students to basics of differential and integral calculus of functions of one variable.
Course outlines
1.Real numbers. Elementary functions.
2. Limit and continuity of functions.
3. Derivative of functions, its properties and applications.
4. Mean value theorem. L'Hospital's rule, Taylor polynomial.
5. Local and global extrema and graphing functions.
6. Indefinite integral, basic integration methods.
7. Integration of rational and other types of functions.
8. Definite integral (using sums). Newton-Leibniz formula.
9. Improper integral. Application of integrals.
10. Sequences and their limits.
11. Rows, criteria of convergence.
12. Introduction to differential equations.
13. Other topics of mathematical analysis.
2. Limit and continuity of functions.
3. Derivative of functions, its properties and applications.
4. Mean value theorem. L'Hospital's rule, Taylor polynomial.
5. Local and global extrema and graphing functions.
6. Indefinite integral, basic integration methods.
7. Integration of rational and other types of functions.
8. Definite integral (using sums). Newton-Leibniz formula.
9. Improper integral. Application of integrals.
10. Sequences and their limits.
11. Rows, criteria of convergence.
12. Introduction to differential equations.
13. Other topics of mathematical analysis.
Exercises outlines
1.Real numbers. Elementary functions.
2. Limit and continuity of functions.
3. Derivative of functions, its properties and applications.
4. Mean value theorem. L'Hospital's rule, Taylor polynomial.
5. Local and global extrema and graphing functions.
6. Indefinite integral, basic integration methods.
7. Integration of rational and other types of functions.
8. Definite integral (using sums). Newton-Leibniz formula.
9. Improper integral. Application of integrals.
10. Sequences and their limits.
11. Rows, criteria of convergence.
12. Introduction to differential equations.
13. Other topics of mathematical analysis.
2. Limit and continuity of functions.
3. Derivative of functions, its properties and applications.
4. Mean value theorem. L'Hospital's rule, Taylor polynomial.
5. Local and global extrema and graphing functions.
6. Indefinite integral, basic integration methods.
7. Integration of rational and other types of functions.
8. Definite integral (using sums). Newton-Leibniz formula.
9. Improper integral. Application of integrals.
10. Sequences and their limits.
11. Rows, criteria of convergence.
12. Introduction to differential equations.
13. Other topics of mathematical analysis.
Literature
[1] J. Stewart, Single variable calculus, Seventh Edition, Brooks/Cole, 2012, ISBN 0538497831.
Requirements
See web page.
Mathematics-Calculus1 A8B01MC1
Credits | 7 |
Semesters | Winter |
Completion | Assessment + Examination |
Language of teaching | Czech |
Extent of teaching | 4P+2S |
Annotation
The aim of the course is to introduce students to basics of differential and integral calculus of functions of one variable.
Study targets
No data.
Course outlines
1. Elementary functions. Limit and continuity of functions.
2. Derivative of functions, its properties and applications.
3. Mean value theorem. L'Hospital's rule.
4. Limit of sequences. Taylor polynomial.
5. Local and global extrema and graphing functions.
6. Indefinite integral, basic integration methods.
7. Integration of rational and other types of functions.
8. Definite integral (using sums). Newton-Leibniz formula.
9. Numerical evaluation of definite integral. Application to calculation of areas, volumes and lengths.
10. Improper integral.
11. Differential equations - formulation of the problem. Separation of variables.
12. First order linear differential equations (variation of parameter).
13. Applications. Numerical aspects.
14. Reserve.
2. Derivative of functions, its properties and applications.
3. Mean value theorem. L'Hospital's rule.
4. Limit of sequences. Taylor polynomial.
5. Local and global extrema and graphing functions.
6. Indefinite integral, basic integration methods.
7. Integration of rational and other types of functions.
8. Definite integral (using sums). Newton-Leibniz formula.
9. Numerical evaluation of definite integral. Application to calculation of areas, volumes and lengths.
10. Improper integral.
11. Differential equations - formulation of the problem. Separation of variables.
12. First order linear differential equations (variation of parameter).
13. Applications. Numerical aspects.
14. Reserve.
Exercises outlines
1. Elementary functions. Limit and continuity of functions.
2. Derivative of functions, its properties and applications.
3. Mean value theorem. L'Hospital's rule.
4. Limit of sequences. Taylor polynomial.
5. Local and global extrema and graphing functions.
6. Indefinite integral, basic integration methods.
7. Integration of rational and other types of functions.
8. Definite integral (using sums). Newton-Leibniz formula.
9. Numerical evaluation of definite integral. Application to calculation of areas, volumes and lengths.
10. Improper integral.
11. Differential equations - formulation of the problem. Separation of variables.
12. First order linear differential equations (variation of parameter).
13. Applications. Numerical aspects.
14. Reserve.
2. Derivative of functions, its properties and applications.
3. Mean value theorem. L'Hospital's rule.
4. Limit of sequences. Taylor polynomial.
5. Local and global extrema and graphing functions.
6. Indefinite integral, basic integration methods.
7. Integration of rational and other types of functions.
8. Definite integral (using sums). Newton-Leibniz formula.
9. Numerical evaluation of definite integral. Application to calculation of areas, volumes and lengths.
10. Improper integral.
11. Differential equations - formulation of the problem. Separation of variables.
12. First order linear differential equations (variation of parameter).
13. Applications. Numerical aspects.
14. Reserve.
Literature
1. M. Demlová, J. Hamhalter: Calculus I. ČVUT Praha, 1994
2.P. Pták: Calculus II. ČVUT Praha, 1997.
2.P. Pták: Calculus II. ČVUT Praha, 1997.
Requirements
See web page.